Processing Math: Done

Aus Online Mathematik Brückenkurs 1

We can factorize the denominators as

y2−2y=yy−2 

y2−4=y−2y+2  [by the conjugate rule]

and then we see that the terms' lowest common denominator is yy−2y+2  because it is the product that contains the smallest number of factors which contain both yy−2  and y−2y+2  .

Now, we rewrite the fractions so that they have same denominators and start simplifying:

y2−4=y−2y+2y2−2y=yy−21y2−2y−2y2−4=1yy−2y+2y+2−2y−2y+2yy=y+2yy−2y+2−2yy−2y+2y=y+2−2yyy−2y+2=−y+2yy−2y+2

The numerator can be rewritten as −y+2=−y−2  and we can eliminate the common factor y−2 .

−y+2yy−2y+2=−y−2yy−2y+2=−1yy+2=−1yy+2